paddle_quantum.finance.pricing

Tools for QMC, option pricing and credit analysis.

paddle_quantum.finance.pricing.qae_cir(oracle, num_ancilla)

Create a QAE circuit based on the oracle given.

Parameters:

  • oracle (Tensor) – input oracle.

  • num_ancilla (int) – number of ancilla qubits used.

Returns:

a circuit used for quantum amplitude estimation.

Return type:

Circuit

paddle_quantum.finance.pricing.qae_alg(oracle, num_ancilla)

Quantum amplitude estimation (QAE) algorithm

Parameters:

  • oracle (Tensor) – an \(n\)-qubit oracle \(\mathcal{A}\).

  • num_ancilla (int) – number of ancilla qubits used.

Returns:

a QAE circuit and \(|\sin(2\pi\theta)|\)

Return type:

Tuple[Circuit, Tensor]

Note

\(\mathcal{A}\) satisfies

\[\mathcal{A}|0^{\otimes n}\rangle=\cos(2\pi\theta)|0\rangle|\psi\rangle+\sin(2\pi\theta)|1\rangle|\phi\rangle.\]
paddle_quantum.finance.pricing.qmc_alg(fcn, list_prob, num_ancilla=6)

Quantum Monte Carlo (QMC) algorithm.

Parameters:

  • fcn (Callable[[float], float]) – real-valued function \(f\) applied to a random variable \(X\).

  • list_prob (List[float]) – probability distribution of \(X\), where the j-th probability corresponds to the j-th outcome.

  • num_ancilla (int) – number of ancilla qubits used. Defaults to be 6.

Returns:

a QAE circuit and an estimation of \(\mathbb{E}[f(X)]\).

Return type:

Tuple[Circuit, Tensor]

class paddle_quantum.finance.pricing.EuroOptionEstimator(initial_price, strike_price, interest_rate, volatility, maturity_date, degree_of_estimation=5)

Bases: object

European option pricing estimator.

Parameters:

  • initial_price (float) – initial price of the asset.

  • strike_price (float) – pre-fixed price of the asset.

  • interest_rate (float) – risk-free interest rate.

  • volatility (float) – dispersion of returns for the asset.

  • maturity_date (float) – date when option is expired.

  • degree_of_estimation (int | None) – degree of price estimation. Defaults to be 5.

Note

Option price is evaluated under the [Black-Scholes-Merton model](https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model).

estimate()

Estimate the European option price using Quantum Monte Carlo (QMC) methods.

Returns:

Risk-neutral price of the given asset.

Return type:

float

plot(dpi=200)

Plot the quantum circuit used in pricing.

Parameters:

dpi (int) – image clarity of the plotted circuit. Defaults to be 200.

class paddle_quantum.finance.pricing.CreditRiskAnalyzer(num_assets, base_default_prob, sensitivity, lgd, confidence_level, degree_of_simulation=4, even_sample=True)

Bases: object

Simulator for credit risk analysis (CRA) speeded up by quantum algorithms

Parameters:

  • num_assets (int) – number of assets.

  • base_default_prob (ndarray) – basic default probabilities of assets.

  • sensitivity (ndarray) – sensitivities of assets.

  • lgd (ndarray) – losses given default (LGD) of assets.

  • confidence_level (float) – level of confidence of computed result.

  • degree_of_simulation (int | None) – degree of simulation of CRA, determining the number of samples of the latent variable. Defaults to be 4.

  • even_sample (bool | None) – whether sample the latent variable by evenly-spaced probability. Defaults to be True.

Note

CRA is simulated under the model given by [Tarca & Silvio](https://arxiv.org/abs/1412.1183). That is, the latent random variable for the market is assumed to follow a standard normal distribution.

estimate_var()

Estimate VaR using the QAE algorithm.

Returns:

the estimated Value at Risk of these credit assets

Return type:

float